# PhD Studentship in Mathematical Sciences

### University of Nottingham - School of Mathematical Sciences

Project Description: Optimising experiments for developing ion channel models.

Supervised by: Dr Gary Mirams & Dr Simon Preston.

This project will be based at the University of Nottingham in the School of Mathematical Sciences.

Mathematical Background: A major challenge in developing mathematical models is parameterising them – using real experimental data to inform the values of things like rates within our models. Getting the correct information can be facilitated by doing the optimal experiment. An even greater challenge is working out the likelihood that the model you have written down is most appropriate from the range of alternative models that could be constructed.

Biological Background: in biological systems ion channel proteins sit in cell membranes and selectively allow the passage of particular types of ions, creating currents. Ion currents are important for many biological processes, for instance: regulating ionic concentrations within cells; passing signals (such as nerve impulses); or co-ordinating contraction of muscle (skeletal muscle and also the heart, diaphragm, gut, uterus, etc.). Mathematical ion channel electrophysiology models have been used for thousands of studies since their development by Hodgkin & Huxley in 1952 [1], and are the basis for whole research fields, such as cardiac modelling and brain modelling [2]. It has been suggested that there are problems in identifying which set of equations is most appropriate as an ion channel model. Often it appears different structures and/or parameter values could fit the training data equally well, but may make different predictions in new situations [3].

Aim: we have been developing novel experimental designs to provide more information about ion channel behaviour from shorter experiments. We would like to improve our techniques – to describe the ion current and also to characterise drug binding to ion channels (which can physically block them and reduce the current that flows to zero, sometimes leading to fatal heart rhythm changes). It is difficult to measure the rate at which drug/ion channel binding occurs and whether it occurs when the channels are open, closed, or both. These factors may be crucial in determining whether novel pharmaceutical compounds are likely to have side effects or not, and there is a need to develop efficient ways to measure them.

Approach: this project will involve computational biophysical modelling (efficient numerical solution of nonlinear ODE systems); the application of statistical techniques to quantify our uncertainty in model parameters and model equations/structure; and some wet-lab laboratory electrophysiology experiments. We will design more information-rich experiments to reduce our uncertainty in the models we develop [4] and work closely with labs to test out experiments we design and improve them.

For informal enquiries email: gary.mirams@nottingham.ac.uk.

Students will be provided with an excellent training environment within the Centre for Mathematical Medicine and Biology and collaborating departments. Students will undertake tailored training, complemented by broadening, soft-skills, wet-lab (where appropriate), and student-led activities. There will also be opportunities for training and exchanges with world-leading partners.

This studentship is open until filled. Early application is strongly encouraged.